Nature's building blocks brought to life

These colourful shapes are part of a project launched last week to create a periodic table of shapes to do for geometry what Dmitri Mendeleev did for chemistry in the 19th century. The three-year project could result in a useful resource for both mathematicians and theoretical physicists to aid calculations in a variety of fields from number theory to atomic physics. But those hoping to buy the wall chart may need to invest in a bigger house as there are likely to be thousands of these basic building blocks from which all other shapes can be formed.

"The periodic table is one of the most important tools in chemistry. It lists the atoms from which everything else is made, and explains their chemical properties," says project leader Alessio Corti, based at Imperial College in the UK. "Our work aims to do the same thing for three-, four- and five-dimensional shapes – to create a directory that lists all the geometric building blocks and breaks down each one's properties using relatively simple equations."

The scientists are looking for shapes, known as "Fano varieties", which are basic building blocks and cannot be broken down into simpler shapes. They find Fano varieties by looking for solutions to a variety of string theory, a theory that seeks to unify quantum mechanics with gravity. String theory assumes that in addition to space and time there are other hidden dimensions and particles can be represented by vibrations along tiny strings that fill the entire universe.

According to the researchers, physicists can study these shapes to visualize features such as Einstein's space–time or subatomic particles. For the shapes to actually represent practical solutions, however, researchers must look at slices of the Fano varieties known as Calabi–Yau 3-folds. "These Calabi–Yau 3-folds give possible shapes of the curled-up extra dimensions of our universe," explains Tom Coates, another member of the Imperial team.

Coates says that the periodic table could also help in the field of robotics. These machines are operating in increasingly higher dimensions as they develop more life-like movements. Robot engineers could use the new geometries discovered for the project to help them develop the increasingly complicated algorithms involved with robotic motion.

The periodic table project is an international collaboration between scientists based in London, Moscow, Tokyo and Sydney, led by Corti at Imperial College London and Vasily Golyshev in Moscow. Given the large time differences involved, the team communicates using social media including a project blog, instant messaging and a Twitter feed. Team member Al Kasprzyk, based at the University of Sydney, says, "These tools are essential. With some of us at working in Sydney while others are asleep in London, blogging is an easy way to exchange ideas and keep up to speed."

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14 comments

Fano varieties

I hope that these new geometries can be used for making processors. These geometries can fill volume in the biggest possible density because the objects are the simplest that can exist and therefore can fulfill volume as much as it is possible.

Are these Fano variety

the same for Relativity transformation? Also are these basic geometries changing with the speed? If yes, then how they look like when they move with c speed or for speed exceeding c ? And if they have special shape for c speed is it limited only for shape of photons with quantum energy? So shapes of Fano variety for its zero speed and speed c can unite Relativity with Quantum theory.

I hope that Fano variety

and their colours can be used to calculate spectral lines of atoms nucleus. If colours represent energy of strings that create Fano varieties then it could be possible. Also here can be used the smallest Fano varieties volume, the volume of geometrical objects that represent nucleus.

Shape family should correspond to what in physics?

If such classification of shapes would have something to do with real physics, such family should correspond to some concrete family of structures in our world.It's about microscopic physics, so the natural target for such correspondence would be our particle menagerie - we should search for a field, which such 'shape family' (topological solitons?) would have some correspondence to at least basic particles (starting from 3 families of spin 1/2, simplest charge has spin,...), but I've seen only one such approach (ellipsoid field).

Let's get back to the reality ...

John, it's not a problem to find a theory with nice looking knots/strings/soliton constructions ... the problem is to find such theory which could also be considered as a physical one: - which works exactly as EM+gravity far from particles (by the way defining charge, magnetic moment, mass inside given surfaces),- which natural constructs of field have quantized spin, charge(topological?), come in three families,- which handle with e.g. gluing electric field inside charge in physical way: continuous and without infinites (for example by deforming in into looking differently interaction like weak/strong(GUT)),- for which given set of quantum numbers identify concrete configuration of field - particle (even distinguishing neutral kaons...) - which family somehow agrees with our particle menagerie(not less, not more!) and their behaviors, - such nontrivial configurations have nonzero rest energy, what through Lorentz invariance becomes their inertial mass and somehow deform gravitational mass to became also gravitational mass, - which have some internal clock/zitterbewegung to have also wave nature,- ... ?Do you disagree with such basic requirements for such constructions to be worth consider as a physical theory?They appears quite naturally in simple ellipsoid field, but can your knots or constructions from this article even try to get near some reasonable physical requirements?

building blocks of what?

If those shapes are assumed to be the building blocks of matter, then naturally they can not contain any hidden dimensions within them, because if they do, then space is contained within matter rather than matter within space. On the face of it, this counter argument appears logical. However, in reality, there are infinite dimensions within any subatomic particle of matter, because matter particles are singularities within which the space-time continuum does not exist. Our appreciation of the four dimensions of space-time is the result of our material nature and hence our dependence on global coordinate system in the space-time continuum when viewing the world. This statement would no doubt be ambiguous to many, but then the human mind is subject to signal modulation, which fuzzes the true picture of physical reality.

Is chemistry only Mendeleev table?

Do not exist also chemical structures that we can derived from atoms nucleus? Is it possible to substitute electron binds for property of nucleus? Maybe exist symmetry between electron configuration of atom, its electron binds possibility and between nucleus configuration. I know Mendeleev table is the basic, but here exist also nucleus crystal lattice and most of matter and thus also energy is bind in this nucleus lattice.

Examples wanted

If these shapes are supossed to be universal atomic shapes, why dont you show a wellknown shape and how it could be decomposed into these atoms. Just in case you were asleep when you learned about Fano shapes in scool.

Nature's building blocks brought to life

I am wondering how these shapes relate to the interesting shapes described in the chemistry of carbon. There is some understanding of those shapes, and even some theories about how the shapes relate to physical properties and chemical behaviors. Of course there undoubtedly are properties that we have not seen or understood yet, but it would be educational for the rest of us to see these descriptions related to what is already known and even familiar.